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The question on continuum mechanis is solved below. In case of
any query please revert. Kindly upvote, thank you :-)
![[ou] + [ou]= [4 ? (Xn+x3) O Zã (+XB) - < x2] hã (Xz+x3) Zá [X2+X3) -X, 222 (x, +X 3) 2X, at (0, 2,-1) Could come se to 23 Str](http://img.homeworklib.com/questions/bc237520-7101-11eb-be37-e9c987bd7ea9.png?x-oss-process=image/resize,w_560)
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3. For the infinitesimal deformation defined by the following displacement field: u; = a*(X, + X3)...
1. Calculate the infinitesimal and Green strain matrices for the following position function x1] [1.2 0.2...
1. Calculate the infinitesimal and Green strain matrices for the following position function x1] [1.2 0.2 0.21 1 x X20.2 1.3 0.1X2 30.9 0.5 1 IX3 Also, find the displacement gradient tensor, the uniaxial small and Green strains along the direction of the vector: 1
4. Given the deformation field of x3 2X1 + X2 + 3X3 1 Calculate (a) The...
4. Given the deformation field of x3 2X1 + X2 + 3X3 1 Calculate (a) The stretch tensor, U (b) The rotation tensor, R
1). It is found that the displacements in a component are described by x} + v(x*...
1). It is found that the displacements in a component are described by x} + v(x* – x3) VX, X2 XX3 u, (x), X2, X3) u, (x7, X2,x;) uz(X, X2, X3) = 2a where a and v are constants. Determine the strain components in the component. = a a 2). The strain tensor at a material point in a steel component is obtained from an FEA as -180 -242 0 E = -242 -3500 x 10-6 0 0 0 Assuming...
The displacement field in a steel machine component (Young’s modulus, E = 210 GPa and Poisson’s...
The displacement field in a steel machine component (Young’s modulus, E = 210 GPa and Poisson’s ratio, ? = 0.33) is given (in metres) by the following expressions: ux = c(x2 + ?) + 2c uy = 2cx2 − cy uz = c? + 5c? where c = 10−4. For a point (x, y, z) positioned at (1, 1, 1) calculate a) The strain components; [4 marks] b) The stress components and sketch a stress element showing how they act;...
3. A consumer has a utility function defined over three goods, U(x1,x2,x3). At a given set...
3. A consumer has a utility function defined over three goods, U(x1,x2,x3). At a given set of prices and income (p1,p2,p3), a. Can all three goods be necessities b. Can one good be inferior and the other two luxuries c. Find the income elasticity of good 1 if s2 = 0.2, s3 = 0.5, n2 = 2, and n3 = 1, where sj is the budget share of good j and nj is the income elasticity of good j.
show steps please! (1 point) u(x, t represents the vertical displacement of a string of length...
show steps please!
(1 point) u(x, t represents the vertical displacement of a string of length L = 20 with wave equation 16. time t = Utt at position x along the string and at Find u(x, t) if a. the initial velocity of the string is 0 and the rightmost position is held at a vertical displacement of 1 and released b. the initial velocity is a constant -5 and the vertical displacement is 0 c. the initial velocity...
3. Consider the vector field A = (x – z)i + (x3 + yz)j – 3xyềk....
3. Consider the vector field A = (x – z)i + (x3 + yz)j – 3xyềk. Use Stokes' theorem to calculate S/CD x A) . nds where S is the surface of the cone z = 2 - V x2 + y2 above the zy plane. You may use the formula n cos" u du = – cos”- u sin u + 2 -1 [ cos”-2 u du.
A displacement field is given by u-0.01y2 in, v-0.03yz in, and w-0.01 x (4 + 6x2)...
A displacement field is given by u-0.01y2 in, v-0.03yz in, and w-0.01 x (4 + 6x2) in. Determine the Von-Mises stress at point (1,02), İfE-30e6 psi and v 0.3
PIUVICU JEU 12, DUC 24 JCPECHuel 201 1. Given a temperature field defined the function T...
PIUVICU JEU 12, DUC 24 JCPECHuel 201 1. Given a temperature field defined the function T = 280.0 +0.002x +0.004y2 +0.00982, compute the change in temperature for a displacement of 100m in the northwesterly direction and 50m in the vertical direction 2. If VT is the gradient of temperature, show that the maximum variation of T associated with displacement dS occurs when the displacement vector is in the same direction as the gradient. 3. Chart the vector fields defined by...
X=0 x = 1/2 x= L u U2 Uz (a) Trial solution for a 1-D quadratic...
X=0 x = 1/2 x= L u U2 Uz (a) Trial solution for a 1-D quadratic elastic bar element can be written as follows: ū(x) = [N]{u} where, [N] = [N1 N2 N3] and {u} u2 13 1 and Ni L2 L2 [N] and {u} are known as interpolation function matrix and nodal displacement, respectively. (272 – 3L + L´), N= = (22- La), Ns = 12 (2=– LE) Derive the expression for element stiffness matrix, (Kelem) and element force...
1. Calculate the infinitesimal and Green strain matrices for the following position function x1] [1.2 0.2 0.21 1 x X20.2 1.3 0.1X2 30.9 0.5 1 IX3 Also, find the displacement gradient tensor, the uniaxial small and Green strains along the direction of the vector: 1
4. Given the deformation field of x3 2X1 + X2 + 3X3 1 Calculate (a) The stretch tensor, U (b) The rotation tensor, R
1). It is found that the displacements in a component are described by x} + v(x* – x3) VX, X2 XX3 u, (x), X2, X3) u, (x7, X2,x;) uz(X, X2, X3) = 2a where a and v are constants. Determine the strain components in the component. = a a 2). The strain tensor at a material point in a steel component is obtained from an FEA as -180 -242 0 E = -242 -3500 x 10-6 0 0 0 Assuming...
show steps please!
(1 point) u(x, t represents the vertical displacement of a string of length L = 20 with wave equation 16. time t = Utt at position x along the string and at Find u(x, t) if a. the initial velocity of the string is 0 and the rightmost position is held at a vertical displacement of 1 and released b. the initial velocity is a constant -5 and the vertical displacement is 0 c. the initial velocity...
3. Consider the vector field A = (x – z)i + (x3 + yz)j – 3xyềk. Use Stokes' theorem to calculate S/CD x A) . nds where S is the surface of the cone z = 2 - V x2 + y2 above the zy plane. You may use the formula n cos" u du = – cos”- u sin u + 2 -1 [ cos”-2 u du.
A displacement field is given by u-0.01y2 in, v-0.03yz in, and w-0.01 x (4 + 6x2) in. Determine the Von-Mises stress at point (1,02), İfE-30e6 psi and v 0.3
PIUVICU JEU 12, DUC 24 JCPECHuel 201 1. Given a temperature field defined the function T = 280.0 +0.002x +0.004y2 +0.00982, compute the change in temperature for a displacement of 100m in the northwesterly direction and 50m in the vertical direction 2. If VT is the gradient of temperature, show that the maximum variation of T associated with displacement dS occurs when the displacement vector is in the same direction as the gradient. 3. Chart the vector fields defined by...
X=0 x = 1/2 x= L u U2 Uz (a) Trial solution for a 1-D quadratic elastic bar element can be written as follows: ū(x) = [N]{u} where, [N] = [N1 N2 N3] and {u} u2 13 1 and Ni L2 L2 [N] and {u} are known as interpolation function matrix and nodal displacement, respectively. (272 – 3L + L´), N= = (22- La), Ns = 12 (2=– LE) Derive the expression for element stiffness matrix, (Kelem) and element force...
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